Cubatures of precision and for hyperrectangles

Author:
Dalton R. Hunkins

Journal:
Math. Comp. **29** (1975), 1098-1104

MSC:
Primary 65D30

MathSciNet review:
0388738

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Abstract: It is well known that integration formulas of precision for a region in *n*-space which is a Cartesian product of intervals can be obtained from one-dimensional Radau (Gauss) rules. The number of function evaluations in these product cubatures is . In this paper, an algorithm is given for obtaining cubatures for hyperrectangles in *n*-space of precision 2*k*, in many instances , which uses nodes. The weights and nodes of these new formulas are derived from one-dimensional generalized Radau rules.

**[1]**W. Robert Boland and C. S. Duris,*Product type quadrature formulas*, Nordisk Tidskr. Informationsbehandling (BIT)**11**(1971), 139–158. MR**0292295****[2]**Richard Franke,*Minimal point cubatures of precision seven for symmetric planar regions*, SIAM J. Numer. Anal.**10**(1973), 849–862. MR**0343544****[3]**D. R. Hunkins,*Product type multiple integration formulas*, Nordisk Tidskr. Informationsbehandling (BIT)**13**(1973), 408–414. MR**0341819****[4]**A. H. Stroud and Don Secrest,*Gaussian quadrature formulas*, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1966. MR**0202312**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1975-0388738-X

Keywords:
Approximate integration,
cubature,
hyperrectangles,
*n*-cube,
orthogonal polynomials,
polynomial precision

Article copyright:
© Copyright 1975
American Mathematical Society